Star clusters in independence complexes of graphs

2010/07/02 by Barmak, Jonathan Ariel · 3 citations
#05C10 #05C69 #55P15 #57M15 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1007.0418

Abstract

We introduce the notion of star cluster of a simplex in a simplicial complex. This concept provides a general tool to study the topology of independence complexes of graphs. We use star clusters to answer a question arisen from works of Engström and Jonsson on the homotopy type of independence complexes of triangle-free graphs and to investigate a large number of examples which appear in the literature. We present an alternative way to study the chromatic number of a graph from a homotopical point of view and obtain new results regarding the connectivity of independence complexes.

Cited by

• Independence Complexes of Hexagonal Grid Graphs
• Closed neighborhood complexes of graphs
• On independence complexes of graph products

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